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Title: A matrix approach to Sheffer polynomials
Author: Aceto, Lídia
Cação, Isabel
Keywords: Sheffer polynomials
Binomial type polynomials
Appell polynomials
Creation matrix
Generalized Pascal matrix
Issue Date: 2017
Publisher: Elsevier
Abstract: This paper deals with a unified matrix representation for the Sheffer polynomials. The core of the proposed approach is the so-called creation matrix, a special subdiagonal matrix having as nonzero entries positive integer numbers, whose exponential coincides with the well-known Pascal matrix. In fact, Sheffer polynomials may be expressed in terms of two matrices both connected to it. As we will show, one of them is strictly related to Appell polynomials, while the other is linked to a binomial type sequence. Consequently, different types of Sheffer polynomials correspond to different choices of these two matrices.
Peer review: yes
DOI: 10.1016/j.jmaa.2016.08.038
ISSN: 0022-247X
Appears in Collections:CIDMA - Artigos
CHAG - Artigos

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